Laboratory studies of the grinding and rheology of coal—water slurries

RICHAkD Cent+

K&EL

Research; The Dow Chemical Company,

(Receivedbctober

Midland,. MI 48640 (U.S.A.)

1,.1981)

SUMMARY

The laboratory ball mill grinding of coalwater slurries is described for three coals. Emphasis is placed on the measurement of specific mtes of breakage for various opemting conditions_ Corresponding rheological information is also presented based on data collected using a rotational viscometer. A rheological explanation of the influence of various slurry fluidity conditions on the specific mtes of breakqge is presented. This rheological approach has proved useful in both the identification of suitable chemicals for increasing breakage rates in coal-mineral slurry grinding and in the plant scale implementation of dense slurry grinding systems.

INTRODUCTION

The grinding of coal-water slurries is currently of increasing industrial importance due to a number of factors which include environmental constraints requiring the partial liberation and removal of sulfur from coals before combustion, the use of pulverized coal-water slurries to replace oil in cpmbustion equipment, and the development of coal gasification/liquefaction processes which require coal-water slurries as feed. The use of coalwater slurries in combustion or gasification/ liquefaction normally requires a high density slurry containing the smallest amount of water consistent with slurry humping and spraying. For these reasons a program of investigation of the grinding of dense slurries with the use of chemical additives was begun at Dow Chemical in 1967. This program has

*Presented at the 1982 National AIME February 14 - 18, Dallas,.Texas, U.S.A.

Meeting,

led to the commercial application of grinding additives for the grinding of dense mineral slurries in copper, gold, taconite, etc. ore grinding [l] _ However, understanding the grinding of dense coal and mineral slurries has proved to be difficult due to several phenomena, especially the phenomenon of significant changes in the rates of breakage of these brittle materials as slurry fluidity is changed_ This paper demonstrates that there is a consistent pattern of change in specific rates of breakage of coal in dense slurries with controlled variations in slurry fluidity. By matching rheological data with laboratory grinding results, it is possible to identify directly slurry conditions that correspond to: (i) slowing down of breakage rates, (ii) the occasional acceleration of breakage of some sizes and (iii) conditions where chemical additives will increase rates of breakage. Some of the concepts are the same as those previously reported by Klimpel and coworkers [2 - 53, and can be summarized as follows_ The net production rate of material less than some specified size (e.g. kg/h of minus 325 mesh) was used as an index of mill production in a standard batch mill test, with a given feed mater-i& and feed size and given mill and mill conditions. Using this criterion, the following facts were established: (i) The normal range of low slurry density, low viscosity gave no variation in mill production. (ii) Grinding of a somewhat higher viscosity slurry could give increased production_ The higher viscosity was obtained by increase in slurry density and by size distribution control. (iii) Too high viscosity gave decreased production. This was associated with non-firstorder grinding, that is, a slowing-down of grinding rates as the grinding proceeded, due to the production of fines giving increased slurry viscosity. @ Ekavier Sequoia/Printed

in The Netherlands

. 268

1:

(iv) Certain water-soluble chemicals allowed the effect in (ii) to be extended to higher slurry viscosity and even higher production rates before the effect of (iii) became controlhng. These conclusions are verified and extended, -using moq sophisticated rheological analysis, in this paper_

EXPERIMENTAL

PROCEDURE

AND

RESULTS

The laboratory mill used was 200 mm i-d.with avolume of 5800 cm3, fitted with hffrs. The ball charge was 140 one-inch diameter balls with a bulk volume of 2290 cm3 (40% loading) and avoid volume of 870 cm3 (38%). AR tests were run at 60 r.p.m. with a constant slurry volume loading of approximately 700 cm3_ Variations in the percent solids were achieved by changing the water-to-solids ratio to give 700 cm3 total slurry volume. The weight of coals were calculated on as-received coal. not dry coal_ The coals studied are given in Table 1. To assist in analyzing the results it is vahrable to use the concepts of first-order breakage rates and primary breakage distribution [6] _ The rate of breakage of a given size range of particles (in this study, a d/2 screen interval) is proportional to the amount of that size present when grinding is first-order. Thus:

Measuring. the disappearance of material from this size as a fun&ion of time, using lo= linear plots, will directly indicate two impor- _. tad. factors: (i) if the plot is linear, the-size. fraction i is breaking in a first-order_manner; the negative slope gives the Si value; (ii) _if the_ plot is not linear but flattens ar~_g.rindirig proceeds (e.g. as fines build up and viscosity increases) then a slowing-down of breakage is occurring. As the slurry volume is held constant, the weight in the m=Z w varies between tests. Thus, the two measures of production rate to be used in comparisons are the absolute rate of breakage SW and the final net weight produced less than some size, expressed per unit of grind time_ A higher value of SW shows higher breakage r&es. The suite of fragments produced by breakage of a given size without further rebreakage of the fragments is termed the primary breakage distribution. Numbering size intervals from 1 for the largest size, 2 the next size interval, em_, the primaty breakage distribution is represented by bii, that is, the fraction of just broken j material which falls into smaller size interval i. Combining specific rates of breakage with primary breakage distributions to allow for repeated breakage of all fragments gives the well-known batch grinding equation

c71: dWi(f)/dt=-SiWi(t)

i-l

+ 2

Rate of breakage of size j = SiWj( t)61r where §i is the specific rate of breakage (fraction per unit time) of size i, Iy is-the mill hold-up, and Wi(f) is the weight fraction of sizei material at grinding time t. Thus, if the starting feed contains ~~(0) as the top size, dwj(t)/dt

= -Ssiwj(t)

log Wi(t) = log ~~(0) -

(&f/2.3)

b&jwi(t),

i=l i>l

(1)

n>i>j>l

where the nth interval is the material less than the smallest sieve size used. Solution of this set of equations with the starting feed conditions, wi(9), gives predictions of the size distributions expected from first-order grinding for given values of Si, bii.

TABLE 1 coal studies CGssification

-As received Moisture

Coal A, anthracite CoalB,medium volatile bituminoti Coal C, sub-bit&iinous.

Proximate

%

Specific

2-4 3.0 11.1

’

. -

gravity

Volatile

l-55

4.2

1.34

21.6

1.30

39.4

analysis, dry basis

matter 96

.-

Fixed carbon A

-Ash%

87-O.

8.8

75.2

3.2

54.7

5.9

.269

0.7

=0.264 SW=150

min-’

g/min

OS S2,_,,=0.208

0.2

= NO

SVJ=l52 glmin I

chemical

2

4

No chemical

e With chemical

l With chemical 0

mizr g!min

0.3

6

10

8

12

0

2

4

6

8

10

12

Time. minures

Time. minuws

Fig_ 1. First-order plots for batch grinding of 20 x 30 mesh coal B with and without a polycarboxylate cheinical: 57-O wt.% solids_

Fig. 4_ First-order plots for batch grinding of 20 mesh coal B with and without a poIycarboxyiate ical: 67-6 wt.% solids.

30 chem-

x

1.0

0.7 S2,.,,=0.253 SlV=*26

min”

0.5

g/Jmin b : 2

0.3

Cs-

SW=134

g'min

0.2 S30.,o=0.176

min”

SW=109 glmin NJ chemical 0.1 0

2

4

6

8

10

12

0

Fig. 2_ First-order plots for batch grinding of 20 mesh coal B with and without a polycarboxylate ical: 60.6 wt.% so!ids.

30 chem-

x

1.0 0.7

0.5 = ;i g

’

glmin

/

I 0.2

4

6

8

10

12

Fig. 5. First-order plots for batch grinding of 20 mesh coaI B with and without a polycarboxylate ical: 72.3 wt.% solids.

30 chem-

x

The detailed experimental techniques involved in such testing, including the calculation of Si and bii parameters from experimental data, have been completely outlined elsewhere [8] and will not be repeated here. In brief, a test consists of grinding identical closely sized feed charges of weight W for a range of grinding times. After each grind, the material in the mill is completely removed and sized. The b<,i values are calculated from data from a small time f of grinding; the weight remaining in the largest size fraction is used to calculate S1 ; and a record is kept of all the weight fractions, Wi (t). Figures 1 through 5 give first-order disappearance plots for a 20 X 30 mesh (I.S.O.) fraction of coal I3 ground in an increasing sequence of slurry densities (57.0 - 72.3%

FLY-S,,.,,=O.259min SW=138

0.3

2

Time. ninures

Time. minures

,&o_,o=Q.2?1

mi

0.1 0

2

4

6

8

10

12

Time, minutes

Fig_ 3_ First-order plots for batch grinding of 20 mesh coal B with and without a polycarboxylate ical: 64.1 wt.% solid.s.

30 chem-

X

_

220

I-

TABLE

~: :

..

2

SpecificratesofbreakageSandahsolutebreakage~tesSWforvariousco~asmeasured~byon~ize appearancemethod Meshsize

Coal %sOIids

&acG_qndis-

Chemical (kg/t)

Weightof charge(g)

Initial Sslope (min-l)

Initial Final SW Sslope (glmin)

(min‘-I)

120 137 112 185 195 188

same as initial same as initial O-088

65

same as initial 0.336 0.081

173 47

._

-..

F&al SW Wmin)

by=t-

byvot

A A A

58.7 66.7 76.8

47.8 56.4 68.1

20x30 20X30 20x30

-

516 608 735

C C C

56.0 63.2 70.1

49.5 56.9 64.3

20x30 20x30 20x30

-

448 515 582

0.233 0.226 0.152 0.412 0.378 0.288

B B B B

57-O 57.0 60.6 60-6

49-8 49-8 53-4 53-4

20x30 20x30 20x30 20x30

0.5 0.5

464 464 498 498

0.270 0.270 0.253 0.253

125 125 126 126

Same as initial -sameas initial same as initial same as initial

B B B B

64.1 64-1 67.6 67-6

57.1 57-l 60.9 60-S

20x30 20 x30 20x30 20x30

0.5 0.5

533 533 568 568

0.259 0.271 0.264 O-268

138 145 150 152

sameasinitial sameasinitial 0.208 same as initial

118

B B

72-3 72.3

66.0 66.0

20x30 20x30

0.5

616 616

O-194 0.218

120 134

0.087 0.176

54 109

B B B B

60.6 60-6 60.6 60.6

53.4 53.4 53.4 53.4

12x16 12x16 12x16 12x16

0.5 -

498 400* 400* 400**

O-417 0.525 0.504 0.527

208 261 251 263

same asinitial 0.424 0.421 0.426

212 209 212

*Totalcbargecousistedof400gof12 X 16meshfractionand98gof400meshcoaL **Plus 2.0 kg/tofachemical thickener,hydroxymethylcelhdose. solids by weight) with and without the presence of a carboxylate chemical known to influence coal slurry rheoiogy [5 J _ The 57.0 and 60.6% data, Figs. 1 and 2, show *&at the breakage was first-order and the chemical had no effect. The 64.1% data, Fig. 3, also show that breakage was first-order, with the S value with chemicaI being somewhat larger_At 67.6% solids, Fig. 4, grinding without chemical gave non-first-order, slowing-down behavior, while with chemical Erst-order breakage was stilI occurring, with the highest absolute breakage rate SW = 152 g/min. Finally, at 72.3% solids, Fig. 5, grinding without chemical gave extreme non-first-order behavior, while with chemical some &king-down of rate occurred, but as in the previous two figurss, the rate of breakage with chemical was higher_ LTabIe 2 gives the-data obtained for the three coals, with the most complete examination being for coal IL The msuhs clearly show the four conclusions outlined in the Introduction_ .. -_4 more compIetk.methodof anaIy&s is to.dekmine. independemdy the Si- and bii para-

meters for the coal and then use the solution of the first-order batch grinding equation to predict size distributions at various tires of grind, from a prespecified feed distribution_ Direct comparisons of predicted and experimental product size distributions can then be made and the detection of changes in breakage rates can be made on the basis of alI the data, not just the top size-data (see later). Table 3 gives the breakage parameters determined using techniques described elsewhere [S] _ It was found for each coal that Sj a ~7, that is, si = a(x&X#

(3)

TABLE3 First-orderbreakagep-

etersforcoalsgroundil

200 mm i.d_ batch ball mill coal

01

A;authracite 0.91 B;me$_voL bit-O.88 C, sub-bit.

0.78

9

?-

P

=

0.43 0.47 0.57

0.59 0.51 0.43

2.8 2.3. 2.1

varies depending on mill conditions

-_: -.

_. --

:

:.

-.271

.The~cbmukttive primarybreakagedistributions, .-_. _

fittedtheempiricalfunction

r:hangesin preferentialgrinding of particle sixeswereobserved,onlychangesinthescale ofSivalues.Table 3 showstbattbemisaconGistentpatterninbothcz andthe ~I;,J parametersasafunctionofcoalrank;alowering nfrankincreasestherelativerateofgrinding offinersizes(smallercr)whileproducing also afinerprimaryfragmentdistribution(smaller -yandlarger@).

70 -

SO-

i

1 ! i 5 j

1

I

t

Iill 1

I 3

I111111 5

I 10

III 30

1 50

Grinding Time. minur.5

Fig. 6. Weibuli plots for coal B shuries (20 X 30 mesh) at 60.6 and 64.1 wt.% solids showing experimental data us_ prediction assuming first-order breakage. 0 Experimental. -prediction; no chemical added; 60.6 wt.%, 53-4 vol.% solids. w Experimental, --prediction; chemical added; 64.1 wt.%, 57.4 vol.% solids.

The b, values were found to be constant andnormalizable in the regionwherefirstorder breakage is occurring,thatis, b2= = b3.2 = b4.3, etc.; b3.1 = bsz3, etc. Similar testingin mineralslurry grmdinghasshown

thatthemeasuredBi.ivaluesforbreakagein high density slurrieshave a relativelyfiner primaryfragmentdistribution(a.higher~ and smaller =y)than for lower density slurries_ The.only parameter which was found to vz&yasaresultofslurrydensitychange,with or witholit chemical, was the value of a in Sj = a(~~/840 pm)Q; a was constax& thus no

*I

I

11111

1

I 3

I

I

II1111 5

10

I 30

1

I1

59

Grinding Time. minutes

Fig. 7. Weibull plots for coal B slurries (20 X 30 mesh) at 67.6 and 72.3 wt.% solids showing experimental data us. prediction assuming first-order breakage_ w Experimental, - - - prediction; no chemical added; 67-6 wt.%, 60.9 vol.% solids. + Experimental, -prediction; chemical added; 67.6 wt.%, 60.9 vol.% solids. w Experimental ,______prediction; no chemical added; 72.3 wt.%, 66-O vol.% solids_ 0 Experimental, prediction; chemical added; 72.3 wt.%, 66.0 vol.% solids. Figures 6 and7show,forcoalB,tbecomputer(predicted)andexperimentalresultsof weightpercentundersizefor70and400U.S. mesh screensizesplotteduersus grindingtime, plotted on a Weibull plot [9]. Deviations (slowing-down) from first-orderbreakage appear as abending-down of experimental valuesawayfromthecomputedpredictions, andhigherbreakageratesgivehighercurves. Theclosenessofpredicted versus experimental datafortbelowerslurrydensities(60_6,64.1% solids)indicate the accuracy oftheSj, bi,i

272

0.2

2-

a

0.1

0

I

I

I

I

I

1

2

3

4

5

6

Time. minutes

Fig. 8. First-order plots of 60.6% weight slurries of coal B ground in an S-in. batch ball mill. = f2 x 16 mesh; 0 12 X. 16 mesh with 2.0 kg hydroxymethylcellulose/t;12 x 16 mash with 400 mesh material present;. 12 X 16 mesh with 400 mesh materiai present plus 0.5 kg polycarboxylate/t.

parameters used and the validity of the firstorder breakage hypothesis. In Fig. 7 the prediction is good for the 67.6% slurry ground _with chemical, but the same slurry ground without chemical shows a slowing-down of breakage, at longer grind times (see aLso Fig. 4_) Figure 7 also shows that for the 72_3% slurry, significant slowing_doWn is occurring without chemical, while with chemical the production of fines is higher but also slowing down, which is again consistent with the data in Fig. 5. Similar results were obtained for coals A and C. Figure 8 shows the effect on breakage of 12 X 16 mesh coal of increasing the slurry viscosity by using a chemical thickener or by adding fine material to the feed_ It appears that there is an initial fast.er rate of breakage, followed by return to the normal slope of the curve. This initial increase in breakage rate may be allied to the acceleration of breakage r&e of larger.sizes which has been observed. [lo; 111 under some conditions. Figure ~9 shows. the Weibuh plot .of the .data. The percent less than 70 mesh for the thickened

*_

I

I IIll 1

1

I111111

3

5

I

II 30

10

5a

Grinding Time. minurn

Fig. 9. Weibull plots of 60.6% weight slurries of coal B showing experimental data us. prediction assuming first-order hypothesis_ l Experimental, -prediction; no 400 mesh present at t = 0; 60.6 wt.%, 53.4 vol.% solids. v Experimental, --prediction; 400 mesh present at t = 0; 60.6 wt.%, 53.4 vol.% solids.

slurry is higher than for tine unthickened, showing that the larger sizes (> 70 mesh) are breaking faster than normal. However, the percent less than 400 mesh is higher initially, then it starts to fall away from the first-order prediction and approach the normal values, indicating that smaller sizes may be breaking at usual rates. RHEOLOGICAL

PROCEDURE

AND

DATA

The difficulties of measuring nonNewtonian slurry rheology properties of particle suspensions are well known [12,13] _ In the work presen’ted here, two instruments were employed: a Brookfield RVT viscometer wilih a T bar and a helipath stand, and a modified Haake RV3 rotational viscometer using the MV sensor system. The first device, while admittedly giving primarily comparative da--proved useful in la_boratory screening as weII aspiIot plant and fuU scale pltit testing. The second device is not as convenient but it does give semi-quantitative data which can

50

55

60

65

56 Solids By Volume

Fig. 10. Viscosity increases of various coal slurries as a function of percent solids where the particle size make-up consists of a maximum size of 20 U.S. mesh and an approximate slope of one on a log fraction less than size us. log size @II) plot.

help to identify and correlate different slurry conditions with grinding behavior_ The rheological data reported in this paper will be limited to three simple cases: slurries made up of a closely sized sieve fraction; slurries made up of a mixture of sizes down to 5 Crrnwith a size distribution of an approximate straight line with a slope of one on a log-log (Schubmann) plot, called the ‘broad distribution in the following discussion; and a few slurries having a closely sized sieve fraction plus the addition of fines and/or chemical thickener. Figure 10 shows the variation of Brookfield viscosity with slurry density for the broad distribution of the three coals, including the values for coal B in the presence of a polycarboxylate chemical. The rapid increase of viscosity of all the coals in the neighborhood of 60% by volume of solids is obvious- Coal A has clearly the smallest increase in viscosity with increasing percent solids while coal C has the highest rate of increase, which indicates it should have the greatest tendency to exhibit a slowing-down of breakage rate with increasing slurry density_ Figure 11 compares the Weibull

plots for coals A, B, C at slurry densities which show slowing-down, adjusted in the time scale to superimpose the first-order region. It is clear that the slowing-down occurs approximately at the same accumulation of fines in the three cases, but the volume percent solids ranks in the order A, B, C, that is, in the order expected for similar viscous properties from Fig_ 10. It is concluded [l - 41 +&at grinding in regions of slurry density where a small increase causes a large increase in Brookfield viscosity will cause a slowingdown in the specific rates of breakage and the production of fines. The data from the rotational viscometer were obtained under suZiciently controlled operating conditions and known geometric configurations to enable plots of shear stress uers~s rate of shear to be constructed for comparison with the types of behavior shown in Fig. 12. Pseudoplastic slurries may or may not have a yield value, and when shear stress T is plotted uensus shear rate A, a curve results that has a decreasing slope with increasing rate of shear, and generally approaches a limiting slope at

274.

Time.

minutes

Fig_ 11. Comparron of W&bull plots for three coals (16 x 20 mesh feed) at slurry densities which give slowingdown of breakage rates_ 0 Cod A, 68-l vol_% solids;~ coal B, 66-O vol.% solids; m coal C, 64.3 vol.% solids.

higher shear rates. Dilatant slurries exhibit the opposite behavior, that is, an increasing slope of T versus A. A common method of mathematically describing both of these types is the Ostwald-deWaele or Power Law model: T_ = KA”

(5)

where 6: and n are constants for a particular slurry_ The constant I(is referred to as the consistency; the higher the value -of R, the more viscous the slurry. The constant n is caUeh the ftow index, which is a measure of the degree of departure from Newtonian behavior (n .= 1); .k < 1 gives pseudoplastic behavior and rz> 1 dilatant behavior_ Figukes 13 1 16 Show the results of the rheological chan%&erization of the 20 X:30 &h fraction slurries and the broad diktribution slurries for c&-B. &rves e-given for each slurry with andwithout -the carbo~ylate ch_emical;for slurry densities corrkpondzng to the grhid.i.ng~sts~re~brt&d earlier.

Rate

Of Shear

Fig. 12. Shear stress us-shear rate curves for timeindependent non-Newtonian slurries.-

_Figure 13 shows the rheological data for -the lowest pulp density slurries of coal B (57_0%s0lids by weight). The shrrriesexhibited dilatant~~character(n > .-1) with no yield value, the closely sized. slurries were-more dilatant th&n the: broader sized slurries, and the addi-tiori of the carboxylate chemical consistently dimiriished -the. sl& --dilat&t character- -.

275 4om

I -----

3oon -

0

20

40

60

El

IOU

0

-----

I

L

2ox3nomem 2oxxmeshwi*ctlemiQl sroaddisuituo’on Broad diibodw!

20

shear Rate. secanb’

I

I

I

I

I

1

..

tim

dxmical

40 Shear

60 Rate.

80

loo

seco”d-’

Fig. 15. Plot of shear stress us. shear rate for various coal B slurries with 20 mesh largest particle size present: 67.6 wt.% solids.

Fig. 13_ Plot qf shear stress us. shear rate for various coal B slurries with 20 mesh largest particle size present: 57.0 wt.% solids.

1 r =

___

3500

---

-

-6300 _--__

a-

i

t 0

20

40

60

hear

Rake. seccnb’

I 60

I

lea

0

20

40

60

80

100

shear Rate. semnd-’

Fig. 14. Plot of shear stress us_ shear rate for various coal B slurries with 20 mekh largest particle size present: 64-l wt_% solids_

Fig. 16_ Plot of shear stress us_ shear rate for varioxzs coal B slurries with 20 mesh largest particle size present: 72.3 wt.% solids.

In all of the experiments, the grinding always followed the first-order hypothesis when the slurry was of the dilatant type. Figure 14 shows the rheological data for the 64.l%_solids slurries with and without chemical_ There was increasing pseudoplastic character of the slurries at this higher pulp density but the closely sized slurries had a larger n than the broad distribution slurries_ The addition of chemical again caused a decrease in R; the associated grinding data (Figs_ 3 and 6) still showed first-order breakage even though some of the slurries were exhibiting pseudoplastic behavior with no yield value. The absolute breakage rate (SiVJ increased over the 57.0% solids case. When the above observation is evaluated in the light of other test data, it is generally true that

when the slurry character is changed from dilatant to pseudoplastic without creating significant yield values then there is almost always an accompanyingincrease in the breakage rate SW and the mill production_ Figure 15 shows the rheological data for the 67.6% solids slurries_ The increasing pseudoplastic behavior is again evident, but now both slurries without chemical are beginniug to exhibit a yield stress. The addition of chemical removed this yield stress. Thus, the appearance of a significant yield value is a direct indicator of the beginning of the slowingdown of breakage rate. Finally, Fig. 16 shows data for the most dense slurry, 72.3% solids by weight. The slurries all exhibited a significant yield value which could be partly, but not completely,

276

20

0

60

P shear

a0

1m

t2ar.e. second-l

Fig_ 19_ Plot of shear stress us_ shear rate as a func tion of grind time for an initial feed of 50 X 60 mesh coal B at 64.1 wt.% solids.

Fig. 17_ Plot of shear stress us. shear rate for various coal B shn-ries with-12 mesh largest particle size present: 60-6 wt.% solids_

DISCUSSION

AND

CONCLUSIONS

There are three controllable factors which decide the rheological properties of a slurry: (i) slurry density ; (ii) particle size distribution; (iii) chemical environment. The second factor has two interrelated facets: the shape of the particle size distribution (which controls the packing behavior) and the fineness of the distribution (finer particles increase inter-particle forces and increaseviscosity). Factors (ii) and

0.3

0.2 0

2

4

6

8

10

12

Time. minutes

Fig_ 18_ First-orderplots for batch grinding of 50 mesh coal B at 64.1 wt.% solids.

X

60

reduced by the addition of the chemicalWhen the slurry density and/or particle size make-up of the slurry gives a yield value that is too large to be eliminated by the particular concentration of chemical being added, then grinding at that slur?y density, even with chemical, wiU be accompanied by a slowingdown of breakage rate. The data of Fig. 17 correspond to the grinding results of Figs. 8 and 9. The deliberate addition of fines and/or thickeners which changed the slurry rheology from dilatant to pseudoplastic without creating a-large yield value caused an incretie in the breakagerates. Thisis similar to the behavior when the slurry density was increased from 57% to 64%; Figs. 1 and 3, which gave increases in SW; see Table 2.

(iii) are changing during the batch grinding tests, because the size distributions are obviously changingand because the production

of fresh surface area will take up unadsorbed chemical_ The rheological tests were carried out under conditions corresponding to the starting slurries, and it must be realized that the effect of increasing slurry density in the test sequence will continue during the grinding test as the material grinds finer and gives higher slurry viscosity. Figures 18 and 19 demonstrate this change of factors (ii) and (iii) on an initial charge of 50 X 60 mesh coal B being ground at 64% solids by weight .over a period of time, Figure 18 shows the disappearance from the 50 X 60 mesh fraction, with i.nitiaHirst-order grinding followed at longer grind times by the slowingdown of breakage rate. Figure 19 gives the corresponding rheological data which show the slurry changing from weakly pseudoplastic with no yield value at time zero to pseudoplastic, with a significant yield value at longer grind times.

277

In+xpreting the data in this light, the following conclusions ca+ be drawn: (i) &X&y coals and mineral slurries exhibit dilatant character at relatively low slurry densities, less than 40 - 45% solids volume for typical size distributions; closely sized solids give more dilatant character than broad distributions(ii) In this dilatant region, grinding is firstorder, and absolute rates of breakage SW do not vary duringthe grinding or from one slurry density to another_ (iii) Increasing slurry density causes a trend toward pseudoplaStic behavior_ At a given slurry density, more pseudoplastic character can be developed by increasing the solids packing efficiency (by adding a proportion of fines or controlling the size distribution [ 14, 153 ), by the use of a bulk thickening agent, or by the use of chemicals to modify viscosity(iv) When a slurry exhibits pseudoplastic behavior without a yield s’tress, then grinding is first-order with higher absolute rates of breakage SW than in corresponding dilatant systems. (v) Grinding aid chemicals that work best in practice are those which maintain pseudoplastic behavior in the slurry without associated yield stress, or which reduce the yield stress in a dense pseudoplastic slurry. (vi) When grinding is performed on a very dense slurry, the yield stress increases rapidly and leads to non-first-order breakage with a slowing-down of breakage rates. The increased rates of breakage observed with higher slurry density are probably due to higher solid packing in the ball-ball collision zone plus the pseudoplastic rheology. On the other hand, the development of high yield stress and high viscosity will allow the slurry bed to absorb impact like a sponge, without efficient fracture of the particles in the slurry. The most advantageous use of chemicals to modify slurry rheology to increase output from amill appears to be in dense suspensions, to take advantage of high solid content and

pseudoplastic rheology without the disadvantage of the development of high yield stress. A paper describing a series of industrial scale grinding tests, on open and closed circuits, coupled with the rheological concepts of this work, is currently being prepared [IS]. ACKNOWLEDGEMENTS

The author is indebted to The Dow Chemical Company, and to his coworkers, for their support of this work. In addition, thanks are given to Professor L. G. Austin of The Pennsylvania State University for his helppful comments on experimental grinding techniques and methods of data presentation. REFERENCES

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R. Klimpel and W_ Manfroy, Znd Eng_ Chem. Process Des Dev_, 17 (1978) 518 - 523_ R_ Kliipel, Proc Symp. on Fine ParficZes Processing, AIME, 1980, pp_ 1129 - 1152. M. Katzer, R. Klimpel and J. Sewell, &fin. Eng., 33 (1981). R. Klimpel and L. Austin. Powder TechnoL. 31 (1982) 239. W_ Manfroy and R. Klimpel, U.S. Pat. 4.Z26.276; 4.126.277; 4,126,2X3; 4.136,830; 4,162,044; 4.162.045; 4.274,599. L. Austin, Powder Technot_. 5 (1971) 1 - 17. P. Luckieand L. Austin,Mine:l Sci. Eng.. 4 (1972) 24 - 51. L. Austin, R. Klimpel and P. Luckie, The Process Engineering of Size Reduction, AIME, to appear in 1982. L. Austin, K._ Shoji, V. Bhatia and R. Aplan, Znt J. Miner. Process., 1 (1974). M_ Berube, Y. Berube and R. Houillier, Powder TechnoL, 23 (1979) 169 - 17s. L. Austin, personal communication_ E. Wasp, J. Kenny and R. Gandhi, Solid-Liquid Flow, Trans. Tech_ Publication, 1977. R. Bird, W. Stewart and E. Lightfoot, Transport Phenomena, Wiley, New York, 1960. F. Aplan and H. Spedden, Proc. 7th Znt Miner. Process. Congr., Z (1965) 103. R_ Datta, Ph. D. Thesis, Pennsylvania State Univ., 1977. R. Klimpel, Some industrial scale experiences using chemical additives in dense slurry wet grinding, in preparation_